Aperture effects in 2.5D Kirchhoff migration: A geometrical explanation

Abstract

Seismic images obtained by Kirchhoff time or depth migration are always accompanied by some artifacts known as migration noise, migration boundary effects, or diffraction smiles, which may severely affect the quality of the migration result. Most of these undesirable effects are caused by a limited aperture if the algorithms make no special disposition to avoid them. Strong amplitude variation along reflection events may cause similar artifacts. All of these effects can be explained mathematically by means of the method of stationary phase. However, such a purely theoretical explication is not always easily understood by applied geophysicists. A geometrical interpretation of the terms of the stationary‐phase approximation in relation to the diffraction and reflection traveltime curves in the time domain can help to develop a more intuitive understanding of the migration artifacts. A simple numerical experiment for poststack (zero‐offset) data indicates the problem and helps to demonstrate the effects and the methods to avoid them.